[[Quite confusing and interesting]]

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Dear everyone

If a production function is homothetic, we can prove that its TRS is constant, so elastisity of subsititution=dln(tX1/tX2)/TRS(t)=dln(X1/X2)/TRS, so its elastisity of subsititution must be constant, so we can say this production function is a CES function, and can be written as

y=(X1^1/p + X2^1/p)^1/p

And we know this function is homogeneous of degree 1.

However, we know a homothetic function is not necessarily be homogeneous of degree 1.

Then, what is the matter here?

Thanks

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关键词：interesting Confusing interest quite Using interesting quite Confusing

你使用CES方程有问题，应该是（x1^{1/p}+y1^{1/p}）^{p}才是一次齐次的。它之所以是一次齐次的，在于CES函数的特定性质，要求替代弹性必须是不变的。